Nuclear Half Life: Calculations
Summary
TLDRThis educational script explains the concept of half-life in radioactive decay using examples of radium to radon, tritium to helium-3, and thallium to lead. It covers calculations for remaining mass, percentage, and fraction after specific half-lives, emphasizing a step-by-step approach. The script also introduces the process of determining half-life duration when given initial and final masses over a known time.
Takeaways
- 📚 The half-life of radium is 11 days, and after 44 days (4 half-lives), 7.5 grams of a 120-gram sample would remain.
- 🔢 After 44 days, 6.25% of the original radium sample would be left.
- 🔄 The fraction remaining after 44 days of radium's half-life is 1/16, which is equivalent to 6.25%.
- 🕒 Tritium has a half-life of 12.3 years, and it takes 61.5 years for an 80-gram sample to decay to 2.5 grams.
- 📉 If 3.125% of tritium remains, it also takes 61.5 years for the decay, indicating 5 half-lives have passed.
- 🔢 To find the half-life of thallium-207, which decays to lead, start with 200 grams and observe it takes 20 minutes to reduce to 12.5 grams, indicating a half-life of 5 minutes.
- 📊 The process of decay can be visualized through charts showing the amount of substance left after each half-life.
- 🧮 Half-life problems can be solved using simple division for time or multiplication for fractions, but more complex problems may require exponents and logarithms.
- ⏳ The concept of half-life is crucial for understanding radioactive decay and can be applied to various isotopes like radium, tritium, and thallium.
- 🔬 Radioactive decay problems can be approached by considering the physical amount, percentage, or fraction remaining after a given number of half-lives.
Q & A
What is the half-life of radium-222 decaying into radon?
-The half-life of radium-222 decaying into radon is 11 days.
If you start with 120 grams of radium, how much will be left after 44 days?
-After 44 days, which is equivalent to 4 half-lives, 7.5 grams of radium will be left.
How can you calculate the percentage of a substance left after a certain number of half-lives?
-You start at 100% and reduce it by half for each half-life that passes. After 4 half-lives of radium-222, 6.25% of the original amount will be left.
What fraction of the original amount of radium-222 will be left after 44 days?
-After 4 half-lives, 1/16 of the original amount of radium-222 will be left.
How long does it take for 80 grams of tritium to decay to 2.5 grams?
-It takes 61.5 years for 80 grams of tritium to decay to 2.5 grams, considering each half-life is 12.3 years.
What is the half-life of tritium decaying into helium-3?
-The half-life of tritium decaying into helium-3 is 12.3 years.
If you start with 200 grams of thallium-207, how long does it take for it to decay to 12.5 grams?
-It takes 20 minutes for 200 grams of thallium-207 to decay to 12.5 grams.
What is the half-life of thallium-207 decaying into lead?
-The half-life of thallium-207 decaying into lead is 5 minutes.
How can you determine the half-life of a substance if you know the initial and final amounts and the time taken for the decay?
-You can determine the half-life by dividing the total time taken by the number of half-lives that occurred, as shown with thallium-207 where 20 minutes divided by 4 half-lives equals a 5-minute half-life.
What is the relationship between the number of half-lives and the remaining percentage of a substance?
-The remaining percentage of a substance after a certain number of half-lives is the original percentage divided by 2 for each half-life that has passed.
How can you calculate the time it takes for a substance to decay to a certain fraction of its original amount?
-You multiply the half-life of the substance by the number of half-lives needed to reach the desired fraction, as shown with tritium where 12.3 years times 5 half-lives equals 61.5 years.
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